Structural Grading and Characteristic Value of the Moso Bamboo Culm Based on Its Minimum External Diameter

Abstract

Bamboo culm has been regarded as a traditional element in construction; meanwhile, it has great potential for the construction of rural houses to achieve green and low-carbon development. However, traditional bamboo houses are usually constructed according to previous experience, and it is hard to design bamboo houses in a standard way. Structural grading of the bamboo culm is an essential work to achieve standardization design. Grading the Moso bamboo culm (P. edulis) based on its minimum external diameter is proposed in this paper. The geometric, physical and mechanical properties of 883 Moso bamboo culms with three different treatment processes were measured and analyzed, namely untreated, with chemical preservatives and heat treatment. It was found that the external diameter of the Moso bamboo culm could be determined by the perimeter in practice. The treatment process has a great influence on the geometric, physical and mechanical properties. Bamboo culms with three different treatment processes could be divided into five, five and four grades, respectively. Meanwhile, based on measurement data, the characteristic values of each grade are presented, including the wall thickness, external and internal taper, linear mass, nominal density and compressive strength. The minimum chemical treatment factor is 0.785, 0.662 and 0.649, while the minimum heat treatment factor is 0.722, 0.644 and 0.877 for wall thickness, linear mass and nominal density, respectively. The treatment factor for compressive strength is 1.12 and 1.52 of chemical treatment and heat treatment, respectively. This study may aid establishing technical specifications and a standard design method for Moso bamboo structural building.

1. Introduction

The construction industry has become one of the key areas of global carbon emission reduction with the production and construction process of buildings using industrial materials, such as steel, concrete, and brick. Adopting green building materials, especially biomass material, is an essential way to promote sustainable development of the construction industry. Bamboo, a type of renewable biomass material, has been brought into focus due to its peculiarity of faster growth (mature in 3 to 4 years), light weight, higher mechanical strength, better heat storage and vapor resistance [1,2]. The advantages of bamboo-based buildings in environmental performance, financial performance and practical application have been analyzed in [3,4]. It is demonstrated that bamboo culms are 20-fold more favorable than other materials from a sustainability point of view [3]. There has been a long history of natural bamboo as construction material around the world, especially in the tropics and subtropics, where the bamboo forests are mainly distributed, such as Dai houses in China [5], “Nipa huts” in Philippines, “Mizo houses” in India, and “Bahareque” in Ecuador Nowadays, novel bamboo structure systems with low cost and a low level of technology have been developed and studied to promote the construction of developing countries [6]. Meanwhile, there is still an ocean of bamboo structures constructed by bamboo culms in China—for example, The Fish-Shaped Bamboo Pavilion in International Horticultural Exposition (Figure 1a) and bamboo dwellings (Figure 1b) in rural area. However, not only traditional but modern bamboo structures are constructed on the basis of experience rather than using modern design tools in China, restricting the wider adoption of bamboo culms as structural elements. It is of great significance to establish standards and specifications in the Chinese construction sector [7].

As a type of bio-material, the geometric, physical and mechanical properties of bamboo vary from one species to another, even vary from one to another for the same species [8,9,10,11,12,13,14,15], which are mainly influenced by the number of vascular bundle and moisture from the microscopic level [16]. To achieve the goal of standardized design, the foremost thing is to sort every piece of bamboo into specific grades to reduce the variability [8]. Several attempts have been made to establish grading methods of bamboo culms. The authors of [17] presented a grading process for a batch of fresh bamboo poles based on their diameter and density using the K-means clustering analysis algorithm, in which five diameter grades and four density grades were developed. Yang et al. [18,19] verified the feasibility of quickly checking the density of fresh bamboo using the indentation method and determined the relationship between them. Fresh bamboo poles could be divided into four levels according to indentation strength and the scope of the density of each level could be speculated. Meanwhile, the positive correlation between density and parallel-to-grain compressive strength, bending strength and elasticity modulus in different indentation–strength grades is demonstrated. Yang [20,21] measured the geometric parameters of 200 Moso bamboo poles and divided them into nine grades according to their diameter. It was also pointed out that the wall thickness is another classification index of one-meter bamboo culms, which are raw materials for flattened bamboo. The main aim of the abovementioned studies is determining the usage and process scheme of fresh bamboo poles to improve their utilization rate. Meanwhile, the qualities of engineered bamboo products such as laminated bamboo lumber (LBL) [22], parallel bamboo strand lumber (PBSL) [23] and flattened bamboo [20] could be improved through these grading process. However, the abovementioned methods are not suitable for the bamboo culms used in construction.

ISO 19624-2018 [24] provides the principles and procedures of grading bamboo culms, akin to extant codes for timber, namely visual grading and machine grading. Annex A of ISO 19624-2018 [24] presents an example of application to a visual grading standard for bamboo culms based on external diameter and flexural properties. Trujillo et al. [25,26], Nurmadina et al. [27] and Bahtiar et al. [8], respectively, took Guadua angustifolia Kunth, Gigantochloa apus, Hitam, Andong and Tali bamboo culms as research objects and tried to find indicator properties which can reflect the strength or capacities of bamboo culms. The results proved that diameter, linear mass and density can reliably and safely predict the flexural capacities, compressive capacities and compressive strength, respectively. However, there are still deficiencies in existing studies. Firstly, it is limited that the research on structural grading methods and process of Moso bamboo culms in construction, the most widely distributed bamboo species in China. Secondly, the influence of the treatment process has not been considered. Bamboo culms are supposed to be treated before utilizing. Geometric, physical, mechanical properties and durability may be affected by different treatment strategies, which has been demonstrated by Bui et al. [28]. It is equally important to study the structural grading of bamboo culms with different treatments as natural ones.

The objective of this work is to find an indicator property suit for the structural grading of Moso bamboo culms and provide useful data to design. Grading the Moso bamboo culm based on its minimum external diameter is proposed in this paper. After measuring and analyzing the geometric, physical and mechanical properties of 883 Moso bamboo culms with three different treatments, specific grading standards and the characteristic values of each level are presented.

2. Methodology

2.1. Grading Based on the Minimum External Diameter

Visual grading is a non-destructive and easy way to sort bamboo culms according to their geometric properties in practice. Meanwhile, previous study results have proven that the mechanical properties of bamboo are associated with its geometric dimensions [17,18,19]. Thus, it is quite important and convenient to grade the bamboo culms with a certain geometric character.

Bamboo culms have a similar shape to steel tubes, which are commonly used in construction. During the design process of steel tube structures, specific steel tubes could be selected by diameter and thickness. Thus, the diameter and thickness could be regarded as two key parameters to represent Moso bamboo culms. However, it is well known that the cross-section of the Moso bamboo culm is more the shape of an ellipse ring rather than a standard ring. It is hard to realize standard designing if Moso bamboo culms are regarded as an elliptical cylinder due to the geometric characteristics of bamboo culms vary from one to another as a type of bio-material. To solve this problem, it is better to suppose the Moso bamboo culms are round tubes. Though the area of the ring is larger than the elliptic ring with the same perimeter and wall thickness, the safety design could be achieved by introducing one safety factor which is beyond the scope of this paper. Further, the external diameter and thickness change along the length of Moso bamboo culms. Biased safety results could be obtained by designing according to the minimum external diameter.

Therefore, Moso bamboo culms could be regarded as round pipes satisfying following hypothesis: first, the cross-sectional area varies evenly along the length of the culm. Secondly, the material along the culm is uniformed, the mechanical properties of which could be characterized by design values. Thirdly, the influence of nodes is ignored. Based on this, standard designing could be achieved by dividing the Moso bamboo culms into different groups according to their minimum external diameters.

According to the market research results, we found out that the minimum external diameters of Moso bamboo culms utilized in construction are mainly distributed between 60 mm and 130 mm. Thus, five grades of Moso bamboo culms are presented, namely Φ60, Φ75, Φ90, Φ105, and Φ120. The specific diameter ranges of each grade are shown in

Table 1. Grades of Moso bamboo culms based on their minimum external diameter.

Grade	$\mathbf{Minimum}\mathbf{External}\mathbf{Diameter}{\mathit{D}}_{\mathbf{s}}\mathbf{\left(}\mathbf{m}\mathbf{m}\mathbf{\right)}$
Φ60	$60\le D_{\mathrm{s}}<75$
Φ75	$75\le D_{\mathrm{s}}<90$
Φ90	$90\le D_{\mathrm{s}}<105$
Φ105	$105\le D_{\mathrm{s}}<120$
Φ120	$120\le D_{\mathrm{s}}<135$

. The feasibility of this grading pattern will be verified and the specific geometric characteristic value of each grade will be defined according to actual research data in the following sections.

2.2. Sample Condition

A total of 883 Moso bamboo culms with length of two to three meters without apparent defects and cracks cut from Zhejiang province of China, four years old, were selected as study samples, of which 210 were untreated (UT), 283 were randomly selected to be treated with chemical preservatives (CT) and 390 were randomly selected to be treated through heat treatment (HT) process, namely carbonization, respectively, as shown in Figure 2. There are six steps during the chemical treatment process, namely removing sugar by boiling, drying in the air, boiling with anti-mildew and anti-insect chemical reagent, drying in the air, straightening and painting anti-aging reagent. While there are three steps during the heat treatment process, namely removing sugar by boiling, drying in the air, carbonization with certain temperature, pressure and oxygen concentration. All CT bamboo culms were treated in Hangzhou Bamboo Technology Co., Ltd., Zhejiang, China. while all HT bamboo culms were carbonized in Guangdong Jianzhong New Bamboo Technology Co., Ltd, Guangdong, China. Before measurement, all of bamboo culms were transferred to Tianjin and put in the environment with an average temperature of 10.3 °C and a relative humidity of 58.5% for one month to reach equilibrium in terms of moisture content.

2.3. Measuring and Analysis Method

A total of 16 parameters of each sample were measured, namely length $L$, weight $W$ and external diameter $D_{\mathrm{s},\max }$, $D_{\mathrm{s},\min }$, $D_{\mathrm{l},\max }$, $D_{\mathrm{l},\min }$, thickness $t_{\mathrm{s}1}$, $t_{\mathrm{s}2}$, $t_{\mathrm{s}3}$, $t_{\mathrm{s}4}$, $t_{\mathrm{l}1}$, $t_{\mathrm{l}2}$, $t_{\mathrm{l}3}$, $t_{\mathrm{l}4}$, perimeter $C_{\mathrm{s}}$ and $C_{\mathrm{l}}$ at the base and top of the culm, as depicted in Figure 3. Length and perimeter were measured by the tape, as shown in Figure 4a,d, while external diameter and thickness were measured by the electric caliper as shown in Figure 4b,c. Every culm was weighed by an electronic scale, as shown in Figure 4e.

External diameters of each end are determined by two ways, as shown in Equations (1)–(4), one of which is the average value of two perpendicular measurements made across opposite points on the outer surface, namely $D_{\mathrm{s},\mathrm{avg}}$ and $D_{\mathrm{l},\mathrm{avg}}$, another one is calculated by the perimeter as follows, namely $D_{\mathrm{s},\mathrm{c}}$ and $D_{\mathrm{l},\mathrm{c}}$. The comparison between $D_{\mathrm{s},\mathrm{avg}}$, $D_{\mathrm{l},\mathrm{avg}}$ and $D_{\mathrm{s},\mathrm{c}}$, $D_{\mathrm{l},\mathrm{c}}$ is shown in Figure 5 and

Table 2. The statistical value of $D_{\mathrm{s},\mathrm{c}}/D_{\mathrm{s},\mathrm{avg}}$ and $D_{\mathrm{l},\mathrm{c}}/D_{\mathrm{l},\mathrm{avg}}$.

Name	${\mathit{D}}_{\mathbf{s},\mathbf{c}}/{\mathit{D}}_{\mathbf{s},\mathbf{avg}}$			${\mathit{D}}_{\mathbf{l},\mathbf{c}}/{\mathit{D}}_{\mathbf{l},\mathbf{avg}}$
	Avg.	Var.	CV	Avg.	Var.	CV
UT	1.006	0.00036	0.019	1.008	0.00048	0.022
CT	1.005	0.00011	0.011	1.006	0.00009	0.009
HT	1.007	0.00010	0.010	1.007	0.00035	0.019

Note: Avg., Var., and CV mean average value, variance and coefficient of variation, respectively.

. It can be seen that the difference between $D_{\mathrm{s},\mathrm{avg}}$, $D_{\mathrm{l},\mathrm{avg}}$ and $D_{\mathrm{s},\mathrm{c}}$, $D_{\mathrm{l},\mathrm{c}}$ are generally within 5 percent, verifying the validity of the diameter calculated by the perimeter. Meanwhile, $D_{\mathrm{s},\mathrm{c}}$ and $D_{\mathrm{l},\mathrm{c}}$ are determined just by one measurement, while $D_{\mathrm{s},\mathrm{avg}}$ and $D_{\mathrm{l},\mathrm{avg}}$ are determined by two measurements after signing the locations of diameters with maximum and minimum value. It is obvious that measuring the perimeter is more convenient than measuring maximum and minimum diameters in practice. Therefore, the perimeter is recommended to determine the diameter of the Moso bamboo culm in this study.

$$D_{\mathrm{s},\mathrm{avg}}=\left(D_{\mathrm{s},\max }+D_{\mathrm{s},\min }\right)/2$$

(1)

$$D_{\mathrm{l},\mathrm{avg}}=\left(D_{\mathrm{l},\max }+D_{\mathrm{l},\min }\right)/2$$

(2)

$$D_{\mathrm{s},\mathrm{c}}=C_{\mathrm{s}}/\pi$$

(3)

$$D_{\mathrm{l},\mathrm{c}}=C_{\mathrm{l}}/\pi$$

(4)

Further, the average wall thickness of the smaller and larger ends $t_{\mathrm{s},\mathrm{avg}}$, $t_{\mathrm{l},\mathrm{avg}}$, the degree of change in the outer diameter and the internal diameter along length of the bamboo culm, namely external taper ${\alpha }_{\mathrm{e}}$ and internal taper ${\alpha }_{\mathrm{i}}$, linear mass $q_{\mathrm{e}}$ and nominal density $q_0$ which is the density defined by the weight and the cross-sectional area of the smaller end are calculated based on following formulas.

$$t_{\mathrm{s},\mathrm{avg}}=\left(t_{\mathrm{s}1}+t_{\mathrm{s}2}+t_{\mathrm{s}3}+t_{\mathrm{s}4}\right)/4$$

(5)

$$t_{\mathrm{l},\mathrm{avg}}=\left(t_{\mathrm{l}1}+t_{\mathrm{l}2}+t_{\mathrm{l}3}+t_{\mathrm{l}4}\right)/4$$

(6)

$${\alpha }_{\mathrm{e}}=\left(D_{\mathrm{l},\mathrm{c}}-D_{\mathrm{s},\mathrm{c}}\right)/L$$

(7)

$${\alpha }_{\mathrm{i}}=\left[D_{\mathrm{l},\mathrm{c}}-D_{\mathrm{s},\mathrm{c}}-2\left(t_{\mathrm{l},\mathrm{avg}}-t_{\mathrm{s},\mathrm{avg}}\right)\right]/L$$

(8)

$$q_{\mathrm{e}}=W/L$$

(9)

$$q_0=W/\left(A_{\mathrm{s}}L\right)=4W/\pi L\left[D_{\mathrm{s},\mathrm{c}}{}^2-{\left(D_{\mathrm{s},\mathrm{c}}-2t_{\mathrm{s},\mathrm{avg}}\right)}^2\right]$$

(10)

To reduce the impact of sample size, the Bootstrap method is adopted for statistical analysis of the abovementioned parameters of different grades. The basic idea of Bootstrap is to create an artificial list by randomly drawing elements with replacement from the existing data list, which means some elements will be picked more than once. The sample size of the artificial list is the same as the existing data list. Repeating more than one hundred times, we look at the distribution of the artificial lists. The statistics value can be used to estimate the distribution of the totality. The expectation and variance of each artificial list are computed as follows. In the formula, $a$ presents the sample size of the list.

$$E\left(Y_j\right)=\frac{{\displaystyle \sum _{i=1}^a{y}_{ij}}}{a}$$

(11)

$$S^2\left(Y_j\right)=\frac{{\displaystyle \sum _{i=1}^a{\left[y_{ij}-a\left(Y_j\right)\right]}^2}}{a-1}$$

(12)

2.4. Mechanical Properties Testing

A total of 148, 150 and 141 pieces of the abovementioned three kinds of bamboo culms with short lengths were randomly cut for compression testing. The specimen length ($L_0$) was approximately equal to the minimum external diameter, ranging from 60 mm to 120 mm. Half of the specimens were from the node and others were obtained from the internode. Using the same method as described in Section 2.3, we measured the specimen length, diameter and wall thickness of the smaller and larger ends. The specimen weight was also weighed before testing. All specimens were put in the laboratory for two weeks to achieve equilibrium in terms of moisture content. The temperature of the lab was (23 ± 2) °C and the relative humidity was (30 ± 5)%. An electronic universal testing machine with a capacity of 300 kN was utilized in this study. Two orthogonal stain gauges were attached to the specimen to record the deformation parallel and perpendicular to the fibers. Additionally, the loading rate is set to 1.5 mm/min. Compressive testing was conducted by ISO 22157-2019 [29], as shown in Figure 6. The maximum compressive loads $F_{\mathrm{c}}$ were recorded and the compressive strengths ${\sigma }_{\mathrm{c}}$ were calculated according to Equation (13).

$${\sigma }_{\mathrm{c}}=F_{\mathrm{c}}/A_{\mathrm{s}}=4F_{\mathrm{c}}/\pi \left[D_{\mathrm{s},\mathrm{c}}{}^2-{\left(D_{\mathrm{s},\mathrm{c}}-2t_{\mathrm{s},\mathrm{avg}}\right)}^2\right]$$

(13)

3. Results and Discussion

3.1. Distribution of the Minimum External Diameter

As can be seen in Figure 7, the maximum $D_{\mathrm{s},\mathrm{c}}$ value of three kinds of Moso bamboo culms are 139.3 mm, 147.7 mm and 122.2 mm, respectively, while the minimum value are 60.8 mm, 59.6 mm and 58.9 mm, respectively. $D_{\mathrm{s},\mathrm{c}}$ value of UT and CT are mainly distributed between 60 mm and 135 mm, while the value of HT is mainly distributed between 60 mm and 120 mm. The reason why the minimum external diameter of HT is rarely exceeds 120 mm may be because the heat treatment process causes cross-section contraction. Thus, it is strongly recommended that Moso bamboo culms be graded according to Table 1. UT, CT and PT could be divided into five, five and four groups, respectively. Each group is named by treatment method and grades—for example, UT-60 presents the minimum external diameters of untreated bamboo culms, which are concentrated between 60 mm and 75 mm.

3.2. Distribution of the Wall Thickness

Six different Bootstrap sampling times, namely 100, 500, 1000, 2000, 5000 and 10,000, were adopted to calculate the mean value and the variance of the wall thickness $t_{\mathrm{s},\mathrm{avg}}$ of each grade. The results are shown in

Table 3. Statistics of the wall thickness $t_{\mathrm{s},\mathrm{avg}}$ after Bootstrap sampling (mm).

Name	Grade	Bootstrap Sampling Times
		100		500		1000		2000		5000		10,000
		Avg.	Var.	Avg.	Var.	Avg.	Var.	Avg.	Var.	Avg.	Var.	Avg.	Var.
UT	UT-60	8.48	0.1248	8.48	0.1111	8.48	0.1094	8.48	0.1060	8.48	0.1098	8.48	0.1068
	UT-75	8.95	0.0306	8.95	0.0317	8.96	0.0328	8.95	0.0337	8.95	0.0324	8.95	0.0334
	UT-90	9.96	0.0208	9.96	0.0304	9.98	0.0302	9.97	0.0289	9.97	0.0291	9.96	0.0287
	UT-105	10.38	0.0115	10.40	0.0135	10.39	0.0126	10.39	0.0126	10.39	0.0128	10.39	0.0129
	UT-120	11.23	0.0517	11.19	0.0511	11.18	0.0511	11.20	0.0529	11.20	0.0519	11.20	0.0515
CT	CT-60	6.68	0.1150	6.68	0.0957	6.68	0.0944	6.69	0.0941	6.68	0.0980	6.68	0.0982
	CT-75	7.78	0.0176	7.75	0.0161	7.75	0.0175	7.76	0.0171	7.75	0.0178	7.75	0.0177
	CT-90	8.44	0.0094	8.45	0.0097	8.46	0.0097	8.45	0.0097	8.45	0.0096	8.45	0.0096
	CT-105	9.55	0.0139	9.55	0.0102	9.55	0.0109	9.55	0.0101	9.55	0.0103	9.55	0.0103
	CT-120	11.26	0.0616	11.28	0.0574	11.26	0.0592	11.28	0.0622	11.28	0.0646	11.28	0.0609
HT	HT-60	5.82	0.0068	5.81	0.0073	5.82	0.0072	5.81	0.0072	5.82	0.0074	5.81	0.0075
	HT-75	6.62	0.0144	6.63	0.0134	6.63	0.0135	6.63	0.0123	6.62	0.0126	6.63	0.0126
	HT-90	7.52	0.0204	7.51	0.0088	7.52	0.0092	7.52	0.0085	7.52	0.0091	7.52	0.0088
	HT-105	8.93	0.0227	8.93	0.0281	8.94	0.0257	8.95	0.0275	8.94	0.0276	8.94	0.0272

Note: Avg. represents the mean value, while Var. represents the variance. UT, CT and HT represent bamboo culms with untreated, chemical and heat treatment process, respectively.

. The statistical results tend to be stable when the sampling times are greater than 5000. Considering the reliability of the statistical results and the cost of calculation, 5000 is an appropriate number of samplings. The distribution of $t_{\mathrm{s},\mathrm{avg}}$ after 5000 times Bootstrap sampling is shown in Figure 8. The fitting results show that the distribution of $t_{\mathrm{s},\mathrm{avg}}$ is normal distribution, as the red fitted line depicted in Figure 8. Fifth percentile is regarded as characteristic value and can be computed according to Equation (14), where $\mu$ and $\sigma$ are expected value and standard deviation of normal distribution, respectively. The characteristic value of the wall thickness $t_k$ of each grade is listed in

Table 4. Statistical results of the wall thickness (mm).

Name	Grade	Expected Value	Standard Deviation	Characteristic Value
UT	UT-60	8.48	0.33	7.9
	UT-75	8.95	0.18	8.7
	UT-90	9.97	0.17	9.7
	UT-105	10.40	0.11	10.2
	UT-120	11.20	0.23	10.8
CT	CT-60	6.68	0.31	6.2
	CT-75	7.75	0.13	7.5
	CT-90	8.45	0.10	8.3
	CT-105	9.55	0.10	9.4
	CT-120	11.28	0.25	10.9
HT	HT-60	5.82	0.08	5.7
	HT-75	6.62	0.11	6.4
	HT-90	7.52	0.10	7.3
	HT-105	8.94	0.17	8.7

.

$$f_k=\mu -1.645\sigma$$

(14)

Characteristic values of the wall thickness $t_k$ of Moso bamboo culm from different grades are compared in Figure 9. The wall thickness generally linearly increases with the grade increasing, which means the larger the external diameter, the thicker the wall. The wall thickness significantly decreases after the treatment process. In the same grade, the wall thickness of UT is larger than CT and larger than HT. The ration of $t_k$ after the treatment process to $t_k$ without treatment of each grade is defined as treatment factor of the wall thickness TF_t,i, where t presents the meaning of the wall thickness, i presents the grade number, as listed in

Table 5. Treatment factor of the wall thickness TF_t,i.

	Grade	60	75	90	105	120
Name
UT		1.000	1.000	1.000	1.000	1.000
CT		0.785	0.862	0.856	0.922	1.009
HT		0.722	0.736	0.753	0.853	/

. The TF_t,i of CT varies from 0.785 to 1.009, while the TF_t,i of CT varies from 0.722 to 0.853. It could be inferred that the influence of treatment is weakened gradually with the grade increasing. The results prove that the study of structural grading is essential for Moso bamboo culm products with any new treatment technology.

3.3. Distribution of External and Internal Taper

Conducting the same method to analyze the distribution of external and internal taper after 5000 times Bootstrap sampling, the fitting results prove that the distribution of ${\alpha }_{\mathrm{e}}$ and ${\alpha }_{\mathrm{i}}$ fits for normal distribution, as the red fitted line depicted in Figure 10 and Figure 11. According to the fitting results, the characteristic value of external and internal taper was calculated according to the ninety-fifth percentile and the results are listed in

Table 6. Normal distribution fitting results of external taper (%) after 5000 times Bootstrap sampling.

Name	Grade	Expected Value	Standard Deviation	Characteristic Value
UT	UT-60	0.30	0.03	0.36
	UT-75	0.46	0.03	0.50
	UT-90	0.56	0.01	0.58
	UT-105	0.67	0.03	0.72
	UT-120	0.81	0.05	0.89
CT	CT-60	0.48	0.04	0.55
	CT-75	0.64	0.02	0.68
	CT-90	0.67	0.02	0.70
	CT-105	0.70	0.02	0.73
	CT-120	0.65	0.03	0.70
HT	HT-60	0.55	0.03	0.59
	HT-75	0.58	0.04	0.64
	HT-90	0.59	0.03	0.64
	HT-105	0.76	0.07	0.87

and

Table 7. Normal distribution fitting results of internal taper (%) after 5000 times Bootstrap sampling.

Name	Grade	Expected Value	Standard Deviation	Characteristic Value
UT	UT-60	0.36	0.04	0.42
	UT-75	0.36	0.03	0.41
	UT-90	0.46	0.02	0.49
	UT-105	0.48	0.03	0.53
	UT-120	0.50	0.04	0.56
CT	CT-60	0.41	0.05	0.50
	CT-75	0.54	0.02	0.57
	CT-90	0.44	0.02	0.48
	CT-105	0.40	0.02	0.44
	CT-120	0.35	0.04	0.41
HT	HT-60	0.45	0.02	0.48
	HT-75	0.42	0.03	0.47
	HT-90	0.45	0.03	0.49
	HT-105	0.51	0.06	0.61

, respectively. The characteristic external taper value of the Moso bamboo culm varies from 0.36% to 0.87%, while the internal taper varies from 0.41% to 0.61%.

Comparison of the characteristic external and internal taper ${\alpha }_{\mathrm{e},k}$ and ${\alpha }_{\mathrm{i},k}$ between different grades is shown in Figure 12. ${\alpha }_{\mathrm{e},k}$ of UT increases approximately linearly when the grade varies from 60 to 120, while the value of CT and HT varies smoothly. The ration of ${\alpha }_{\mathrm{e},k}$ after the treatment process to ${\alpha }_{\mathrm{e},k}$ without treatment of each grade is defined as treatment factor of external taper TF_e,i, where e presents the meaning of external taper, i presents the grade number, as listed in

Table 8. Treatment factor of external taper TF_e,i.

	Grade	60	75	90	105	120
Name
UT		1.000	1.000	1.000	1.000	1.000
CT		1.528	1.300	1.207	1.013	0.786
HT		1.017	1.280	1.103	0.888	/

. TF_e,i of CT varies from 0.786 to 1.528, while TF_e,i of CT varies from 0.888 to 1.280. ${\alpha }_{\mathrm{i},k}$ has no obvious variety regulation, but fluctuates at a level of 0.49%. Thus, the characteristic internal taper value of every grade can be considered as 0.49% for convenience.

3.4. Distribution of Linear Mass and Nominal Density

The same method was conducted to analyze the distribution of linear mass and nominal density. Normal distribution fitting results are shown in

Table 9. Normal distribution fitting results of linear mass (kg/m) after 5000 times Bootstrap sampling.

Name	Grade	Mean Value	Standard Deviation	Characteristic Value
UT	UT-60	1.69	0.05	1.61
	UT-75	2.45	0.06	2.36
	UT-90	3.24	0.05	3.17
	UT-105	4.04	0.05	3.96
	UT-120	5.13	0.13	4.91
CT	CT-60	1.26	0.04	1.19
	CT-75	1.72	0.04	1.66
	CT-90	2.21	0.04	2.15
	CT-105	2.76	0.05	2.69
	CT-120	3.40	0.09	3.25
HT	HT-60	1.20	0.02	1.18
	HT-75	1.56	0.02	1.52
	HT-90	2.27	0.04	2.20
	HT-105	3.07	0.06	2.97

and

Table 10. Normal distribution fitting results of nominal density (kg/m³) after 5000 times Bootstrap sampling.

Name	Grade	Mean Value	Standard Deviation	Characteristic Value
UT	UT-60	1035.72	25.55	993.69
	UT-75	1187.61	13.75	1164.99
	UT-90	1199.58	12.99	1178.22
	UT-105	1239.36	10.81	1221.57
	UT-120	1283.99	14.40	1260.30
CT	CT-60	990.04	31.83	937.67
	CT-75	942.51	15.63	916.81
	CT-90	943.33	12.22	923.23
	CT-105	904.77	14.73	880.55
	CT-120	854.18	22.26	817.56
HT	HT-60	1110.32	12.03	1090.53
	HT-75	1053.03	21.05	1018.40
	HT-90	1106.37	17.77	1077.13
	HT-105	1101.57	18.14	1071.73

, respectively. Figure 13a presents the comparison of the characteristic linear mass $q_{e,k}$. $q_{e,k}$ of UT is higher than CT and HT, demonstrating that the weight of Moso bamboo culms will reduce after treatment due to the reduction in moisture content. The ration of $q_{e,k}$ and $q_{0,k}$ after the treatment process to the one without treatment of each grade are defined as treatment factor of linear mass TF_l,i, and treatment factor of nominal density TF_n,i, where l and n presents the meaning of linear mass and nominal density, respectively, i presents the grade number, as listed in

Table 11. Treatment factor of linear mass TF_l,i.

	Grade	60	75	90	105	120
Name
UT		1.000	1.000	1.000	1.000	1.000
CT		0.739	0.703	0.678	0.679	0.662
HT		0.733	0.644	0.694	0.750	/

and

Table 12. Treatment factor of nominal density TF_n,i.

	Grade	60	75	90	105	120
Name
UT		1.000	1.000	1.000	1.000	1.000
CT		0.944	0.787	0.784	0.721	0.649
HT		1.097	0.874	0.914	0.877	/

. TF_l,i of CT and HT varies from 0.662 to 0.739 and 0.644 to 0.750, while TF_n,i varies from 0.649 to 0.944 and 0.877 to 1.097 for CT and HT. With the increase of grades, $q_{e,k}$ increases approximately linearly. The increase rates of CT and HT are slower than that of UT, proving that the effect of the treatment process is greater for Moso bamboo culms with larger external diameter. As can be seen in Figure 13b, the characteristic nominal density value $q_{0,k}$ shows a different pattern with $q_{e,k}$. $q_{0,k}$ of UT increases with the grades while $q_{0,k}$ of CT presents completely different trend. $q_{0,k}$ of HT are much more stable between each grade. The results prove that different treatment methods have a significant effect on the physical properties of bamboo.

3.5. Distribution of Compressive Strength

A total of 439 specimens (148 UT, 150 CT, 141 HT) were subjected to compression test according to ISO 22157-2019 [29]. The mean compressive strength ${\sigma }_{\mathrm{c}}$ of UT, CT and HT is 61.85, 65.82 and 102.61 MPa, respectively (

Table 13. Descriptive statistics of compressive strengths of three kinds of specimens.

Statistics	UT	CT	HT
Number	148	150	141
Max (MPa)	98.77	86.21	156.15
Min (MPa)	37.16	66.14	46.34
Mean (MPa)	61.85	65.82	102.61
5% value (MPa)	41.35	50.37	59.77
Standard deviation (MPa)	13.69	8.44	27.10
Coefficient of variation (%)	22.14	12.83	26.41

), which indicates that the treatment process has great influence on the mechanical properties of the bamboo culm. The compressive strength could be significantly improved after heat treatment, whereas chemical treatment has little influence. However, the heat treatment process causes larger dispersion of compressive strength.

As can be seen in Figure 14, regression results demonstrate the correlation between the minimum external diameter and compressive strength, confirming the rationality of the proposed structural grading method. As the minimum external diameter increases, the compressive strengths show a descending trend no matter the treatment process.

To obtain the characteristic compressive strength value of each grade, 5000 times Bootstrap sampling method and normal distribution analysis were also adopted. Before sampling, data points outside the ellipse band identified as outliers and extreme values were removed, as seen in Figure 15.

Normal distribution fitting results of compressive strength after 5000 times Bootstrap sampling are listed in Table 10. The characteristic value of compressive strength ${\sigma }_{\mathrm{c},k}$ after different treatment, determined by the fifth percentile, was calculated and compared in

Table 14. Normal distribution fitting results of compressive strength (MPa) after 5000 times Bootstrap sampling.

Name	Grade	Mean Value	Standard Deviation	Characteristic Value
UT	UT-60	73.75	2.34	69.90
	UT-75	69.90	1.33	67.71
	UT-90	59.99	1.31	57.83
	UT-105	53.60	0.95	52.04
	UT-120	45.73	1.23	43.70
CT	CT-60	73.74	1.26	71.67
	CT-75	72.38	0.88	70.92
	CT-90	64.89	1.10	63.08
	CT-105	63.51	0.97	61.92
	CT-120	57.25	1.09	55.47
HT	HT-60	119.29	2.77	114.73
	HT-75	112.88	4.59	105.32
	HT-90	88.77	3.29	83.36
	HT-105	81.81	3.54	75.98

and Figure 16. The higher the grade level, the lower the characteristic compressive strength. It is proved that the treatment process has a positive effect on the compressive strength. Comparing with chemical preservatives treatment process, the heat treatment process could significantly improve ${\sigma }_{\mathrm{c},k}$. The ration of ${\sigma }_{\mathrm{c},k}$ after the treatment process to ${\sigma }_{\mathrm{c},k}$ without treatment of each grade is defined as treatment factor of compressive strength TF_c,i, where c presents the meaning of compressive strength, i presents the grade number. Taking the average of TF_c,i, the treatment factor of chemical preservatives treatment and heat treatment could be obtained, namely 1.12 and 1.52, respectively.

3.6. Discussion

According to the abovementioned results, the treatment process has great influence on the geometric, physical and mechanical properties of Moso bamboo culms. The wall thickness, linear mass and nominal density decrease significantly while external taper and compressive strength increase after the treatment process. Compared to chemical treatment, the heat treatment process has greater influence, especially on the nominal density and compressive strength.

The correlation between the minimum external diameter and compressive strength demonstrates the significance of grading bamboo culms according to its minimum external diameter no matter the treatment process. Meanwhile, the larger the grade, the larger the wall thickness and linear mass. However, the compressive strengths show a descending trend as the grade increases.

4. Conclusions

This paper set out to explore a simple and convenient grading method of Moso bamboo culms for structural grading. Structural grading of Moso bamboo culms based on their minimum external diameter is proposed and demonstrated. On the basis of measuring and analyzing the geometric, physical and mechanical properties of 883 Moso bamboo culms with three different treatment processes, the following main conclusions can be drawn as follows.

• The external diameter of the Moso bamboo culm could be determined by the perimeter in practice.
• Based on their minimum external diameter, untreated Moso bamboo culms, Moso bamboo culms with chemical preservatives and heat treatment could be divided into five, five and four grades.
• The characteristic values of the wall thickness, external taper, linear mass, nominal density and compressive strength are different between each grade. The larger the grade, namely the larger the minimum external diameter, the larger the wall thickness, external taper and linear mass, and the smaller the compressive strength. The characteristic internal taper of every grade can be considered as 0.49%.
• The treatment process has a great influence on the geometric, physical and mechanical properties of Moso bamboo culms. The wall thickness, linear mass and nominal density decrease significantly after treatment. The minimum value of chemical treatment factor is 0.785, 0.662 and 0.649, while the minimum value of heat treatment factor is 0.722, 0.644 and 0.877 for the wall thickness, linear mass and nominal density, respectively.
• External taper and compressive strength increase after the treatment process. The treatment factors of chemical treatment and heat treatment are 1.12 and 1.52 for compressive strength, respectively.

This study may aid establishing technical specifications of Moso bamboo structural building, promoting the application of bamboo in civil engineering. However, this paper is a preliminary exploration of bamboo grading, and much more data are needed to validate and improve the results of this study in practice. Meanwhile, the mechanical properties in addition to the compressive strength of each grade of Moso bamboo culms will be studied in the near future.